Generalised gramian framework for model/controller order reduction of switched systems

Hamid Reza Shaker, Rafael Wisniewski

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In this article, a general method for model/controller order reduction of switched linear dynamical systems is presented. The proposed technique is based on the generalised gramian framework for model reduction. It is shown that different classical reduction methods can be developed into a generalised gramian framework. Balanced reduction within a specified frequency bound is developed within this framework. In order to avoid numerical instability and also to increase the numerical efficiency, generalised gramian‐based Petrov–Galerkin projection is constructed instead of the similarity transform approach for reduction. The framework is developed for switched controller reduction. To the best of our knowledge, there is no other reported result on switched controller reduction in the literature. The method preserves the stability under an arbitrary switching signal for both model and controller reduction. Furthermore, it is applicable to both continuous and discrete time systems for different classical gramian‐based reduction methods. The performance of the proposed method is illustrated by numerical examples.
Original languageEnglish
JournalInternational Journal of Systems Science
Volume42
Issue number8
Pages (from-to)1277-1291
ISSN0020-7721
DOIs
Publication statusPublished - 2011
Externally publishedYes

Fingerprint

Order Reduction
Switched Systems
Controller
Controllers
Reduction Method
Petrov-Galerkin
Linear Dynamical Systems
Numerical Instability
Model
Continuous-time Systems
Model Reduction
Discrete-time Systems
Framework
Projection
Transform
Numerical Examples
Arbitrary
Dynamical systems

Cite this

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abstract = "In this article, a general method for model/controller order reduction of switched linear dynamical systems is presented. The proposed technique is based on the generalised gramian framework for model reduction. It is shown that different classical reduction methods can be developed into a generalised gramian framework. Balanced reduction within a specified frequency bound is developed within this framework. In order to avoid numerical instability and also to increase the numerical efficiency, generalised gramian‐based Petrov–Galerkin projection is constructed instead of the similarity transform approach for reduction. The framework is developed for switched controller reduction. To the best of our knowledge, there is no other reported result on switched controller reduction in the literature. The method preserves the stability under an arbitrary switching signal for both model and controller reduction. Furthermore, it is applicable to both continuous and discrete time systems for different classical gramian‐based reduction methods. The performance of the proposed method is illustrated by numerical examples.",
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Generalised gramian framework for model/controller order reduction of switched systems. / Shaker, Hamid Reza; Wisniewski, Rafael.

In: International Journal of Systems Science, Vol. 42, No. 8, 2011, p. 1277-1291.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

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AB - In this article, a general method for model/controller order reduction of switched linear dynamical systems is presented. The proposed technique is based on the generalised gramian framework for model reduction. It is shown that different classical reduction methods can be developed into a generalised gramian framework. Balanced reduction within a specified frequency bound is developed within this framework. In order to avoid numerical instability and also to increase the numerical efficiency, generalised gramian‐based Petrov–Galerkin projection is constructed instead of the similarity transform approach for reduction. The framework is developed for switched controller reduction. To the best of our knowledge, there is no other reported result on switched controller reduction in the literature. The method preserves the stability under an arbitrary switching signal for both model and controller reduction. Furthermore, it is applicable to both continuous and discrete time systems for different classical gramian‐based reduction methods. The performance of the proposed method is illustrated by numerical examples.

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